Research Question: Do medical consultants lead patients to better outcomes?
How many orange Reeses Pieces are in a typical bag of 40?
https://www.rossmanchance.com/applets/2021/oneprop/OneProp.htm?candy=1
Set the Probability of orange to 0.5, the Number of candies to 40, the Number of samples to 1, and choose the Proportion of orange statistic.
Click Draw Samples. How many orange did you get? What is \(\hat{p}_\text{boot}\)? Does it equal \(\hat{p}\)? Is it close?
Now change Number of samples to 99 and click Draw Samples again. When it finishes, make sure Total Samples is 100.
The dotplot that appears should have 100 dots. Use this dotplot to estimate a bootstrap 90% confidence interval for the proportion of orange Reeses Pieces.
Now repeat steps 1-4, but suppose that your bag of candy had 400 Reeses Pieces, 200 of which were orange. How did the confidence interval change?
In a sample of 120 listeners, only 3 were able to correctly guess the tune that was being tapped. (\(\hat{p} = 0.025\))
Simulation:
\[ 0.0417 \quad 0.025 \quad 0.025 \quad 0.0083 \quad 0.05 \quad 0.0333 \quad 0.025 \quad 0 \quad 0.0083 \quad 0 \]